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• W3197826830 abstract "The equitable tree-coloring can formulate a structure decomposition problem on the communication network with some security considerations. Namely, an equitable tree-k-coloring of a graph is a vertex coloring using k distinct colors such that every color class induces a forest and the sizes of any two color classes differ by at most one. In this paper, we show some theoretical results on the equitable tree-coloring of graphs by proving that every d-degenerate graph with maximum degree at most Δ is equitably tree-k-colorable for every integer k ≥ (Δ + 1)/2 provided that Δ ≥ 9.818d, confirming the equitable vertex arboricity conjecture for graphs with low degeneracy." @default.
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• W3197826830 date "2021-08-01" @default.
• W3197826830 modified "2023-10-05" @default.
• W3197826830 title "Equitable Vertex Arboricity Conjecture Holds for Graphs with Low Degeneracy" @default.
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• W3197826830 doi "https://doi.org/10.1007/s10114-021-0663-4" @default.
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